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We analyse the h-step forecasts of futures prices, using the extended two-factor model in Han et al. (On autoregressive measurement errors in a two-factor model. 2021-22 MATRIX Annals (2023)) based on the Schwartz-Smith two-factor model in Schwartz and Smith (Manag. Sci. 46(7), 893–911 (2000)). The two-factor model assumes that the short- and long-term components of the logarithm of futures prices are mean-reverting. Moreover, the short- and long-term factors represent correlated latent Ornstein-Uhlenbeck processes and will be jointly estimated, along with model parameters, using the Kalman filter through the maximum likelihood method. Furthermore, we assume that the error terms in the measurement equation system are inter-dependent and serially correlated. A comparative analysis has been carried out between three models: (a) the reduced-form model in Schwartz and Smith (Manag. Sci. 46(7), 893–911 (2000)), (b) the full model in Han et al. (On autoregressive measurement errors in a two-factor model. 2021-22 MATRIX Annals (2023)), and (c) a hybrid model, where futures prices follow the ARIMA process. In (c), we will use the least squares support vector regression (LS-SVR) method for the prediction of the residuals of the multivariate ARIMA process. Historical daily prices of European Union Allowance (EUA) futures contracts from January 30, 2017, to April 1, 2022, were used for illustration in this study.

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Two-Factor and ARIMA-LS-SVR Models for Forecasting of EUA Futures Prices

  • 会议论文

  • 发表日期：

    2025年

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  • Jun S. Han,
  • Nino Kordzakhia,
  • Pavel V. Shevchenko,
  • Stefan Trück

摘要

We analyse the h-step forecasts of futures prices, using the extended two-factor model in Han et al. (On autoregressive measurement errors in a two-factor model. 2021-22 MATRIX Annals (2023)) based on the Schwartz-Smith two-factor model in Schwartz and Smith (Manag. Sci. 46(7), 893–911 (2000)). The two-factor model assumes that the short- and long-term components of the logarithm of futures prices are mean-reverting. Moreover, the short- and long-term factors represent correlated latent Ornstein-Uhlenbeck processes and will be jointly estimated, along with model parameters, using the Kalman filter through the maximum likelihood method. Furthermore, we assume that the error terms in the measurement equation system are inter-dependent and serially correlated. A comparative analysis has been carried out between three models: (a) the reduced-form model in Schwartz and Smith (Manag. Sci. 46(7), 893–911 (2000)), (b) the full model in Han et al. (On autoregressive measurement errors in a two-factor model. 2021-22 MATRIX Annals (2023)), and (c) a hybrid model, where futures prices follow the ARIMA process. In (c), we will use the least squares support vector regression (LS-SVR) method for the prediction of the residuals of the multivariate ARIMA process. Historical daily prices of European Union Allowance (EUA) futures contracts from January 30, 2017, to April 1, 2022, were used for illustration in this study.